Math Problem Statement

If f(x)=4sinx3+cosxf(x)=4sinx3+cosx, then f'(x)f′(x) =   

f'(3)f′(3) = 

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Chain Rule
Trigonometric Functions

Formulas

Derivative of sin(u) = cos(u) * du/dx
Derivative of cos(x) = -sin(x)
Chain rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)

Theorems

Chain Rule
Derivative of Trigonometric Functions

Suitable Grade Level

Undergraduate Calculus or Advanced High School